Performance Guarantees for Individualized Treatment Rules.

Because many illnesses show heterogeneous response to treatment, there is increasing interest in individualizing treatment to patients [11]. An individualized treatment rule is a decision rule that recommends treatment according to patient characteristics. We consider the use of clinical trial data in the construction of an individualized treatment rule leading to highest mean response. This is a difficult computational problem because the objective function is the expectation of a weighted indicator function that is non-concave in the parameters. Furthermore there are frequently many pretreatment variables that may or may not be useful in constructing an optimal individualized treatment rule yet cost and interpretability considerations imply that only a few variables should be used by the individualized treatment rule. To address these challenges we consider estimation based on l(1) penalized least squares. This approach is justified via a finite sample upper bound on the difference between the mean response due to the estimated individualized treatment rule and the mean response due to the optimal individualized treatment rule.